(a) Field of the Invention
The invention relates to a two-dimensional array waveguide structure, and more particularly, to a two-dimensional array waveguide structure formed by multi-layer circuit process or monolithic integrated circuit process for accomplishing a miniaturized microwave integrated circuit.
(b) Description of Related Art
Miniaturization of microwave integrated circuits has been a research subject for microwave integrated circuit engineers and researchers. Large amounts of distributed elements are employed in microwave circuits, whereas the largest dimensions of the distributed elements approach the wavelengths corresponding to actual operating frequencies such that reducing dimensions of microwave circuits is rather hard to achieve.
One of the most common methods for reducing dimensions is to make a microwave circuit into a monolithic integrated circuit. The thickness of a substrate of a monolithic microwave integrated circuit (MMIC), and dimensions of planar or coplanar waveguide printed on the substrate, may all be reduced three-dimensionally in scale. For example, a typical MMIC formed on a gallium arsenide substrate with a εr coefficient of 12.9 has a substrate thickness to be approximately 100 μm. However, a similar hybrid microwave integrated circuit using a substrate with a εr coefficient of 10.5 and a thickness of 250 μm, has a waveguide line width or a line gap of 250/100×(√{square root over (12.9+1)}/√{square root over (10.5+1)}) times of the former. It is assumed that a propagation constant of the transmission line can be appropriately enlarged and reduced without drastic changes (Maxwell's equation appears to be linear, and hence the above hypothesis should be able to establish). Therefore, the area of a monolithic microwave integrated circuit, can be 0.4×(√{square root over (10.5+1)}/√{square root over (12.9+1)})≈36% times smaller than that of the hybrid integrated circuit using a thicker substrate (K. C Gupta, Ramesh Garg, Inder Bahl, and Prakash Bhartia, “Microstrip lines and Slotlines”, Artech House, Boston London, 1996).
Apart from allowing three-dimensional size reduction, researchers have also utilized lumped elements for serving as quasi-waveguide elements to manufacture passive elements or circuits (George L. Matthaei, Stephan M. Rohifing, Roger J. Forse, “Design of HTS, lumped-element, manifold-type microwave multiplexers”, IEEE Trans. Microwave Theory Tech. vol. 44, pp. 1313-1321, July 1997). Because it is essential that dimensions of a lumped element be much smaller than wavelengths of operating frequencies, the circuit area of an entire passive element is substantially reduced. Lumped elements used as quasi-waveguide elements generally have smaller operating frequency ranges, and are unsuitable for wide-band applications.
Moreover, the characteristic of a wavelength λg of a slow-wave transmission line much smaller than λ0 (λ0 is the wavelength of light velocity, or the wavelength of electromagnetic waves in vacuum) can also be utilized to reduce areas of microwave integrated circuits. The semiconductor portion at the lower section of a microstrip made from a metal-insulator-semiconductor (MIS) transmission line is doped to change distributions of electric field and magnetic field of the microstrip, such that a slow-wave factor (SWF), λ0/λg, is significantly increased (D. Jäger, “Slow-wave propagation along variable Schottky-contact microstrip line,” IEEE Trans. Microwave Theory Tech., vol. MTT-24, pp. 566-573, September 1976. H. Ogawa and T. Itoh, “Slow-Wave Characteristics of Ferromagnetic Semiconductor Microstrip Line,” IEEE Trans. Microwave Theory Tech., vol. MTT-34, pp. 1478-1482, December 1986). Semiconductor processes can produce slow-wave lines having an SWF greater than 10. However, loss of these MIS slow-wave lines are greatly increased due to existence of doping, and such additional loss prohibits extensive applications of the MIS slow-wave lines. Based upon principles similar to those of MIS slow-wave lines, partially changing electric field and magnetic field distributions of transmission lines may also accomplish increase of the SWF. A periodic structure like coplanar waveguide adopts a cross-tie structure to partially produce capacitive loading to further change electric field and magnetic field directions of the waveguide. According to documented records, a SWF as high as 11.6 can be obtained (T. H. Wang and T. Itoh, “Compact grating structure for application to filters and resonators in monolithic microwave integrated circuits,” IEEE Trans. Microwave Theory Tech., vol. 35, pp. 1176-1182, December 1987). Using similar principles, the cross-tie can be reversed by connecting itself with a lower metal layer to produce capacitive loading with respect to the coplanar waveguide, and thus a high SWF of 8 can be achieved according to other references (U.S. Pat. No. 4,340,873).